Remove Parts of a Flat Plane
Ok I came up with the solution by myself, based on new info provided about Boolean modifiers not working on flat planes in answers to my OP.  Instead of trying to model a 2D shape and then extrude it to a 3D shape later, it occurred to me that I should just create the 3D shape in its entirety and then use the Boolean modifier as it's intended to cut out the alcoves from the room.  I created cubes in the dimensions of each alcove, then used snapping to position them relative to the appropriate corner (a fiddly process), then apply the operator.  This has achieved exactly what I wanted.



I guess that if I still wanted a 2D shape then I could have still modelled it as above, then deleted the edges/faces that make it 3D, leaving a flat face in the shape I wanted.